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2-7 Warm Up Problem of the Day Lesson Presentation

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1 2-7 Warm Up Problem of the Day Lesson Presentation
Solving Equations with Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

2 Warm Up Add or subtract. 7 10 5 10 1 5 1. + 3 8 5 16 1 16 2. 2 – 1 8.4 – 0.05 2.35

3 Problem of the Day A computer word is made of strings of 0’s and 1’s. How many different words can be formed using 3 characters? (An example is 010.) 8

4 Learn to solve equations with rational numbers.

5 Additional Examples 1A: Solving Equations with Decimals.
Solve. m = 9 m = 9 Subtract 4.6 from both sides. – 4.6 = 4.4 m = Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. Remember!

6 Additional Examples 1B: Solving Equations with Decimals
Solve. 8.2p = –32.8 8.2p 8.2 = Divide both sides by 8.2 –4 p =

7 Additional Examples 1C: Solving Equations with Decimals
Solve. = 15 x 1.2 x 1.2 = 1.2 • 15 1.2 • Multiply both sides by 1.2 x = 18

8 Check It Out: Example 1A & 1B
Solve. A. m = 3 m = 3 Subtract 9.1 from both sides. –9.1 = –6.1 m = B. 5.5b = 75.9 = b Divide both sides by 5.5 13.8 b =

9 C. Solve. Check It Out: Example 1C y 4.5 = 90 y 4.5 = 4.5 • 90 4.5 •
Multiply both sides by 4.5 y = 405

10 Additional Example 2A: Solving Equations with Fractions
Solve. 2 7 3 7 n + = – n – = – – 2 7 3 7 27 Subtract from both sides. 2 7 n = – 5 7

11 Additional Example 2B: Solving Equations with Fractions
Solve. 1 6 2 3 y = 1 6 = 2 3 + y Add to both sides. 1 6 = y 4 6 1 6 + Find a common denominator; 6. y = 5 6 Simplify.

12 Additional Example 2C: Solving Equations with Fractions
Solve. 5 6 5 8 x = 3 5 6 = 5 8 x 6 5 Multiply both sides by . 6 5 4 x = 3 4 Simplify.

13 Solve. Check It Out: Example 2A 1 9 5 9 n + = –
Subtract from both sides. 1 9 n – = – – 1 9 5 9 19 n = – 2 3 Simplify – . 6 9

14 Solve. Check It Out: Example 2B 1 2 3 4 y – = 1 2 = 3 4 – + y
Add to both sides. 1 2 = y 3 4 2 4 + Find a common denominator; 4. y = 1 1 4 Simplify.

15 Solve. Check It Out: Example 2C 3 8 = 6 19 x 3 8 = 6 19 x 2 3 8 = 6 19
8 3 Multiply both sides by . 8 3 1 x = 16 19 Simplify.

16 = 2 Additional Example 3: Solving Word Problems Using Equations
Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving of the dessert has tablespoon of sugar, how many servings can he make for the party? 2 3 Write an equation: Amount needed for each dessert Amount of sugar Total servings = s 2 3 = 2

17 Additional Example 3 Continued
Now solve the equation. 2 3 = 2 s 2 3 = 2  s 3 2 Multiply both sides by . 3 2 8 3 s = 3 2 24 6 , or 4 s = Simplify. Mr. Rios can make 4 servings.

18 Ratio of car’s tank to van’s tank
Check It Out: Example 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold gallons of gasoline, how much gasoline can the tank in the minivan hold? 2 3 2 31 Write an equation: Van’s gas tank Ratio of car’s tank to van’s tank Capacity of car’s tank = 2 3 31 2 g =

19 Check It Out: Example 3 Continued
Now solve the equation. 2 3 31 2 g = Multiply both sides by . 3 2 31 2 2 3 = g 3 2 g = 93 4 Simplify. 1 4 g = 23 The van’s gas tank holds 23 gallons of gasoline. 1 4

20 Lesson Quiz: Part 1 Solve. 1. x – 23.3 = 17.8 x = 41.1 2 3 3 4 j = –15 5 12 2. j = –14 3 5 1 15 y = 3. 9y = d 3 8 1 2 d = 9 4. = 2 4

21 Lesson Quiz: Part II 2 5 5. Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5 hours


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